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Representation-of-integer-operations

Shr-ulong-uchar-okp

Check if the right shift of a value of type unsigned long by a value of type unsigned char is well-defined.

Definitions and Theorems

Function: shr-ulong-uchar-okp

(defun shr-ulong-uchar-okp (x y)
  (declare (xargs :guard (and (ulongp x) (ucharp y))))
  (shr-ulong-okp x (integer-from-uchar y)))

Theorem: booleanp-of-shr-ulong-uchar-okp

(defthm booleanp-of-shr-ulong-uchar-okp
  (booleanp (shr-ulong-uchar-okp x y)))

Theorem: shr-ulong-uchar-okp-of-ulong-fix-x

(defthm shr-ulong-uchar-okp-of-ulong-fix-x
  (equal (shr-ulong-uchar-okp (ulong-fix x) y)
         (shr-ulong-uchar-okp x y)))

Theorem: shr-ulong-uchar-okp-ulong-equiv-congruence-on-x

(defthm shr-ulong-uchar-okp-ulong-equiv-congruence-on-x
  (implies (ulong-equiv x x-equiv)
           (equal (shr-ulong-uchar-okp x y)
                  (shr-ulong-uchar-okp x-equiv y)))
  :rule-classes :congruence)

Theorem: shr-ulong-uchar-okp-of-uchar-fix-y

(defthm shr-ulong-uchar-okp-of-uchar-fix-y
  (equal (shr-ulong-uchar-okp x (uchar-fix y))
         (shr-ulong-uchar-okp x y)))

Theorem: shr-ulong-uchar-okp-uchar-equiv-congruence-on-y

(defthm shr-ulong-uchar-okp-uchar-equiv-congruence-on-y
  (implies (uchar-equiv y y-equiv)
           (equal (shr-ulong-uchar-okp x y)
                  (shr-ulong-uchar-okp x y-equiv)))
  :rule-classes :congruence)